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Sunday, December 21, 2014

Enlarging (or Decreasing) Circular Blocks

Several people have asked how I drafted the larger blocks in my Steam Punk quilt. It's an application of basic high school geometry. No kidding. The geometric principle is this: similar figures have proportional lengths and congruent angles. That means you always multiply lengths by the same amount while angles stay the same.

Steam Punk quilt with larger and small blocks

How do you do it?

1. Measure your original block and decide how large or small you want the new block.

I won't give the exact measurements of Steam Punk; you'll have to buy that pattern. But let's pretend the original finished block was 4" and the blades intersect the side 1.25" from the corners (Fig. 1 below.)

Fig. 1 - example of original block at 4-inches

2. Calculate the scale factor (new finished block size/original block size) to determine how long the new segments will be. My new block finishes 8" so my scale factor (8/4) is 2.

Draw a new block 8" on each side (4" x 2) and mark the center of the block. Using the scale factor already!

Mark points on all four sides 2.5" from the corners (1.25" x 2). Scale factor again!

Fig. 2 - example of drafting an enlarged circle block

3. Draw lines from the center to these points on the side. (Fig. 3)

Using a compass with the sharp point in the center of the block and the pencil at the side point 2.5" from the corner, draw new curves for the blades. If your compass won't expand that far, use your ruler. Place the end on the center of the block and align the ruler through that 2.5" point.

Notice the measurement on the ruler. On my example it's about 4.25".

Fig. 3 - enlarged block with main lines drawn

4. Now rotate the ruler slowly in an arc, keeping the center at the ruler endpoint. Use your pencil to mark many small dots at the same length until you reach the 2.5" mark on the next side (Figs. 4 and 5.) Connect all those points to mark the blade curve.

Note: If you're making a really large block, use your rotary ruler. This tiny ruler just made the photo easier to shoot and see.

Fig. 4 - drawing a circle or arc on an enlarged block

Fig. 5 - enlarged arc is drawn

Once your block is drafted, check the central angles by placing your original blade and triangle templates on the new block pattern at the center. The sides should line up perfectly. The templates are just shorter than your new length.

The radius of the center circle will also be multiplied by the scale factor. So if it was one-half inch originally, it will be one inch in this example (1/2" x 2).

5 comments:

So you should be visiting geometry classes to show them how to use the principles I learned, and by learned I mean knew long enough for a test, in real life! That's a great needed tute. I realized today, that my follow by email button had disappeared and added it back in. Grr. Hope your holidays are going well now! LeeAnna at not afraid of color

You're too funny! I think we truly learn things when we realize how they apply to our lives. Perhaps the art teacher could ask the math teacher in when they reach this point in art class. And isn’t technology interesting? It’s like Dorothy said, “My! People come and go so quickly around here.” Happy Holidays!

Very interesting Ann! I see someone retained some of what they learned in geometry, LOL. It was one of my favorite subjects. I like your reply to LeeAnna - we do learn better when things apply to our lives!

I liked geometry and statistics best. Funny what strikes a chord, isn’t it?But someone has to ask before I think to write a tutorial. We all think in different ways and there’s lots of artwork I need a tutorial for. I guess our attitude is: If I figure out a method it seems it should be completely obvious to everyone; only other people’s work is unique.Happy New Year.